How to Measure Information: Entropy, KL Divergence and Fisher Information

Why does snow in the Sahara tell us more than an ordinary sunrise? A town’s daily weather reports connect surprise and compression to the cost of a wrong forecast, then to how precisely data can estimate the chance of rain. We develop entropy, KL divergence and Fisher information using probability, logarithms and basic calculus. 0:00 Measuring surprise 2:36 Entropy and shorter codes 5:32 The cost of a wrong belief 9:26 Fisher information and precision 12:19 Three views of information Related lesson: Maximum Likelihood Estimation    • Maximum Likelihood Estimation: Why 7 Out o...   Sources: Shannon, A Mathematical Theory of Communication (1948); Kullback and Leibler, On Information and Sufficiency (1951); Fisher, Theory of Statistical Estimation (1925). Narration is synthesized with Qwen3-TTS using the channel’s Chatterbox voice reference. Music was generated with ACE-Step 1.5.